Fully nonlinear degenerate equations with applications to grad equations

Abstract

We consider a class of degenerate elliptic fully nonlinear equations with applications to Grad equations:(|Du|γM+λ,ΛD2u(x) = f|u ≥ u(x)| in Ωu = g on ∂,where γ≥1 is a constant, Ω is a bounded domain in RN with C1,1 boundary. We prove the existence of a W2,p-viscosity solution to the above equation, which degenerates when the gradient of the solution vanishes.